Quantum Groups, Correlation Functions and Infrared Divergences

TL;DR

This paper demonstrates that in one-dimensional quantum chains with quantum group symmetries, local operator correlation functions typically diverge in the infrared, but quantum group invariant correlations are free of such divergences.

Contribution

It reveals the role of quantum group invariance in canceling infrared divergences in correlation functions of quantum chains.

Findings

Local operator correlations are infrared divergent.

Quantum group invariance cancels divergences.

Invariant correlations are well-defined and finite.

Abstract

We show in two simple examples that for one-dimensional quantum chains with quantum group symmetries, the correlation functions of local operators are, in general, infrared divergent. If one considers, however, correlation functions invariant under the quantum group, the divergences cancel out.